The high court overturned a lower court ruling against the shareholders, who want to represent all investors who bought Halliburton stock between June 1999 and December 2001.

The lawsuit argues that Halliburton deliberately understated the company’s liability in asbestos litigation, inflated how much money its construction and engineering units would bring in, and overstated the benefits of a merger with Dresser Industries. When Halliburton made corrective disclosures, it made the stock price drop and caused investors to lose money, the lawsuit said.

The 5th US Circuit Court of Appeals in New Orleans refused to let the lawsuit go forward as a class-action, saying that to get class-action certification, the shareholders needed to prove “loss causation, i.e., that the corrected truth of the former falsehoods actually caused the stock price to fall and resulted in the losses.’’

But the Supreme Court said that ruling was incorrect.

The case now goes back to the lower court.

“Halliburton looks forward to presenting its arguments before the Court of Appeals,’’ the company said in a statement.